#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; const long long int mod = 1e9 + 7; using lint = long long; lint ipow(lint x, lint p) { lint ret = 1, piv = x; while (p) { if (p & 1) ret = ret * piv % mod; piv = piv * piv % mod; p >>= 1; } return ret; } vector berlekamp_massey(vector x) { vector ls, cur; int lf, ld; for (int i = 0; i < x.size(); i++) { lint t = 0; for (int j = 0; j < cur.size(); j++) { t = (t + 1ll * x[i - j - 1] * cur[j]) % mod; } if ((t - x[i]) % mod == 0) continue; if (cur.empty()) { cur.resize(i + 1); lf = i; ld = (t - x[i]) % mod; continue; } lint k = -(x[i] - t) * ipow(ld, mod - 2) % mod; vector c(i - lf - 1); c.push_back(k); for (auto& j : ls) c.push_back(-j * k % mod); if (c.size() < cur.size()) c.resize(cur.size()); for (int j = 0; j < cur.size(); j++) { c[j] = (c[j] + cur[j]) % mod; } if (i - lf + (int)ls.size() >= (int)cur.size()) { tie(ls, lf, ld) = make_tuple(cur, i, (t - x[i]) % mod); } cur = c; } for (auto& i : cur) i = (i % mod + mod) % mod; return cur; } int get_nth(vector rec, vector dp, lint n) { int m = rec.size(); vector s(m), t(m); s[0] = 1; if (m != 1) t[1] = 1; else t[0] = rec[0]; auto mul = [&rec](vector v, vector w) { int m = v.size(); vector t(2 * m); for (int j = 0; j < m; j++) { for (int k = 0; k < m; k++) { t[j + k] += 1ll * v[j] * w[k] % mod; if (t[j + k] >= mod) t[j + k] -= mod; } } for (int j = 2 * m - 1; j >= m; j--) { for (int k = 1; k <= m; k++) { t[j - k] += 1ll * t[j] * rec[k - 1] % mod; if (t[j - k] >= mod) t[j - k] -= mod; } } t.resize(m); return t; }; while (n) { if (n & 1) s = mul(s, t); t = mul(t, t); n >>= 1; } lint ret = 0; for (int i = 0; i < m; i++) ret += 1ll * s[i] * dp[i] % mod; return ret % mod; } int guess_nth_term(vector x, lint n) { if (n < x.size()) return x[n]; vector v = berlekamp_massey(x); if (v.empty()) return 0; return get_nth(v, x, n); } struct elem { int x, y, v; }; // A_(x, y) <- v, 0-based. no duplicate please.. vector get_min_poly(int n, vector M) { // smallest poly P such that A^i = sum_{j < i} {A^j \times P_j} vector rnd1, rnd2; mt19937 rng(0x14004); auto randint = [&rng](int lb, int ub) { return uniform_int_distribution(lb, ub)(rng); }; for (int i = 0; i < n; i++) { rnd1.push_back(randint(1, mod - 1)); rnd2.push_back(randint(1, mod - 1)); } vector gobs; for (int i = 0; i < 2 * n + 2; i++) { int tmp = 0; for (int j = 0; j < n; j++) { tmp += 1ll * rnd2[j] * rnd1[j] % mod; if (tmp >= mod) tmp -= mod; } gobs.push_back(tmp); vector nxt(n); for (auto& i : M) { nxt[i.x] += 1ll * i.v * rnd1[i.y] % mod; if (nxt[i.x] >= mod) nxt[i.x] -= mod; } rnd1 = nxt; } auto sol = berlekamp_massey(gobs); reverse(sol.begin(), sol.end()); return sol; } lint det(int n, vector M) { vector rnd; mt19937 rng(0x14004); auto randint = [&rng](int lb, int ub) { return uniform_int_distribution(lb, ub)(rng); }; for (int i = 0; i < n; i++) rnd.push_back(randint(1, mod - 1)); for (auto& i : M) { i.v = 1ll * i.v * rnd[i.y] % mod; } auto sol = get_min_poly(n, M)[0]; if (n % 2 == 0) sol = mod - sol; for (auto& i : rnd) sol = 1ll * sol * ipow(i, mod - 2) % mod; return sol; } int main(void) { cin.tie(0); ios::sync_with_stdio(false); long long int n, k, t; vector v,v2; v.push_back(0); cin >> n >> k; for (int i = 0; i < n; i++) { cin >> t; v.push_back(t); } for (int i = n + 1; i <= 3000; i++) { long long int sum = 0; for (int j = 1; j <= n; j++) { sum += v[i - j]; sum %= mod; } v.push_back(sum); } long long int sum = 0; for (int i = 0; i <= 3000; i++) { sum += v[i]; sum %= mod; v2.push_back(sum); } cout << guess_nth_term(v, k) << ' ' << guess_nth_term(v2,k) << '\n'; return 0; }